### Home > PC3 > Chapter 9 > Lesson 9.2.2 > Problem9-120

9-120.

Vectors $\vec { \text{u} }$ and $\vec { \text{v} }$ are perpendicular. If $\vec { \text{v} }= ⟨2, 1 + b⟩$ and $\vec { \text{v} }= ⟨4, 1 − b⟩$ , determine all possible values for $b$.

If two vectors are perpendicular, their dot product is $0$.
Or, they have opposite reciprocal slopes.

Solve $⟨2, 1 + b⟩ · ⟨4,1 − b⟩ = 0$.

$\left(\text{or }\frac{1+b}{2}=-\frac{4}{1-b}\right)$